A limit theorem for a class of stationary increments L\'{e}vy moving average process with multiple singularities

Authors :: Mark Podolskij
Mathias Mørck Ljungdahl
Source :: Ljungdahl, M M & Podolskij, M 2018, ' A limit theorem for a class of stationary increments Levy moving average process with multiple singularities ', Modern Stochastics: Theory and Applications, vol. 5, no. 3, pp. 297–316 . https://doi.org/10.15559/18-VMSTA111, Modern Stochastics: Theory and Applications, Vol 5, Iss 3, Pp 297-316 (2018)
Publication Year :: 2018
Abstract: In this paper we present some new limit theorems for power variations of stationary increment L\'{e}vy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477--4528, Festschrift for Bernt {\O}ksendal, Stochastics 81(1) (2017), 360--383] under the assumption that the kernel function potentially exhibits a singular behaviour at $0$. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653--677] that studied the same mathematical question for the class of Brownian semi-stationary models.<br />Comment: Published at https://doi.org/10.15559/18-VMSTA111 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)

Language :: English
Database :: OpenAIRE
Journal :: Ljungdahl, M M & Podolskij, M 2018, ' A limit theorem for a class of stationary increments Levy moving average process with multiple singularities ', Modern Stochastics: Theory and Applications, vol. 5, no. 3, pp. 297–316 . https://doi.org/10.15559/18-VMSTA111, Modern Stochastics: Theory and Applications, Vol 5, Iss 3, Pp 297-316 (2018)
Accession number :: edsair.doi.dedup.....5d305638fe585e15709f2b39a15509fa

Tools